已知实数a>0,求函数f(x)=[ax^2+3(a+1)x+3a+6] / (e^x)的极值
问题描述:
已知实数a>0,求函数f(x)=[ax^2+3(a+1)x+3a+6] / (e^x)的极值
答
f(x)=[ax^2+3(a+1)x+3a+6] / (e^x)f ‘(x)={[2ax+3(a+1)](e^x) - [ax^2+3(a+1)x+3a+6](e^x)}/[e^(2x)]={[2ax+3(a+1)] - [ax^2+3(a+1)x+3a+6]}/(e^x)=[- ax^2-(a+3)x-3]/(e^x)=[(ax-3)(-x+1)]/(e^x)...